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The antiferromagnetic Ising chain in both transverse and longitudinalmagnetic fields is one of the paradigmatic models of a quantum phasetransition. The antiferromagnetic system exhibits a zero-temperature criticalline separating an antiferromagnetic phase and a paramagnetic phase; thecritical line connects an integrable quantum critical point at zerolongitudinal field and a classical first-order transition point at zerotransverse field. Using a strong-disorder renormalization group methodformulated as a tree tensor network, we study the zero-temperature phase of thequantum Ising chain with bond randomness. We introduce a new matrix productoperator representation of high-order moments, which provides an efficient andaccurate tool for determining quantum phase transitions via the Binder cumulantof the order parameter. Our results demonstrate an infinite-randomness quantumcritical point in zero longitudinal field accompanied by pronounced quantumGriffiths singularities, arising from rare ordered regions with anomalouslyslow fluctuations inside the paramagnetic phase. The strong Griffiths effectsare signaled by a large dynamical exponent $z>1$, which characterizes apower-law density of low-energy states of the localized rare regions andbecomes infinite at the quantum critical point. Upon application of alongitudinal field, the quantum phase transition between the paramagnetic phaseand the antiferromagnetic phase is completely destroyed. Furthermore, quantumGriffiths effects are suppressed, showing $z<1$, when the dynamics of the rareregions is hampered by the longitudinal field.

Griffiths Singularities in the Random Quantum Ising Antiferromagnet: A Tree Tensor Network Renormalization Group Study